## Dr. Alexey Kuznetsov: Research

Another major field of my research interest is self-sustained oscillatory dynamics of protein expression. Most well known robust oscillatory circuits in molecular biology are the circadian clock and the cell cycle engine. Recently, other examples of such circuits have been discovered in many other regulatory processes, such as apoptosis, metabolism and morphogenesis. A question addressed in many recent studies is how specific are these oscillatory circuits and their elements. Experimentally this problem is investigated in the Applied Biodynamics Laboratory headed by James Collins at the Biomedical Engineering Department, BU. In close collaboration with an experimentalist Mads Kaern from the above laboratory, I have constructed a robust, hysteresis-based genetic relaxation oscillator and provided a theoretical analysis of the conditions necessary for single-cell oscillations (Kuznetsov et al., SIAM Appl. Math. 2004). Based on my analysis, I have proposed a modification in the architecture of the gene regulatory network that has substantially increased robustness of the oscillations.

The major property of our genetic oscillator is that it can synchronize with other such oscillators encapsulated in different cells in a population. To design a diffusive coupling between the cellular oscillators and so synchronize them, we have incorporated a transgenic quorum sensing signaling pathway from *Vibrio fischeri*. My analysis has shown that **synchronized oscillations are stable and robust for diffusion of a moderate strength**. I have also found that, surprisingly, **a stronger diffusion can disrupt synchrony** in this population. Increasing diffusion causes the oscillations to cease and heterogeneity in protein concentrations to emerge. Thus, my modeling and mathematical analysis have predicted a nontrivial and unexpected effect of diffusion-mediated structure formation.

To emphasize the impact of this research, I want to note that, in our artificial genetic network, the same system is involved in establishing both population oscillations and structure formation. In our model, the diffusion strength, which determines emergence of the oscillations or heterogeneity, depends on population density. Thus, by this mechanism, **the same genetic circuit** in a population or organism during its growth can transit from synchronous oscillations to stationary patterns, **determining different stages of development**.

As a continuation of this project, I am shifting the focus to **modeling of more natural cellular oscillators**, interactions between them and stochastic nature of cellular processes. Stochastic simulations are very important for validation of robustness, as well as for investigation of new effects introduced by stochasticity. The models formulated in terms of differential equations are faster to simulate, but they use the assumption that all concentrations are continuous in time. However, when the number of molecules is low, degradation or synthesis of one extra molecule leads to a jump-like change in concentration. Stochastic modeling of the circadian clock has ignited a discussion of what properties of the molecular network may contribute to its robustness, and this lead to formulation of several universal mechanisms that protect cells against molecular noise. Therefore, I am going to **combine stochastic and dynamical modeling in my research**.

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